Question

I really need help!

What is the product in simplest form? State any restrictions on the variable. Please show your work.

(y^2 / y - 3) x (y^2 - y - 6 / y^2 + y)

Answer 1

\[\frac{ y^2 }{ y -3 } \times \frac{ y^2 -y - 6 }{ y^2 + y }\]

Answer 2

I'd factor the y^2-y-6, so you can cross out 2 terms.

Answer 3

y^2 - y = 1 I think

So, 1 - 6?

Answer 4

Are you referring to the trinomial? It would be (y-3)(y+2)

Answer 5

yes because

3 x 2 = 6

and 3 - 2 = 1

Answer 6

-3 times 2=-6
-3+2=-1

y^2-y-6

Answer 7

right

Answer 8

I forgot we are dealing with negatives

Answer 9

That's alright

Now you have a y-3 and a y-3, which you cross out

Answer 10

\[\frac{ y^2(y+2) }{ y^2+y }\]

Answer 11

You are now up to there, try to simplify more. (you can )

Answer 12

Okay.

\[y^2 \times y = y^3 \]

Answer 13

Now we got y^3 + 2 over y squared plus y

Answer 14

Good, now try to simplify the denominator

Answer 15

y^2(y+2)=y^3+2y^2

Answer 16

(numerator)

Answer 17

Simplify the numerator or the denominator?

Answer 18

you already did the numerator. your denominator is y^2+y, try to factor it out.

Answer 19

ok

Answer 20

\[y^2 + y = y (y + y)\]

Answer 21

Hmm that's pretty close. but check again.

y(y+y)=y^2+y^2

Answer 22

Oh I see now

Answer 23

Wanna write out your new simplification?

Answer 24

Your almost done

Answer 25

yes, but i'm still trying to simplify y squared plus y. I know it's not that hard but for some reason I can't put my finger on it

Answer 26

y^2+y=

y(y+1)

y times 1=y

Answer 27

Thank you! I didn't think about that

Answer 28

Are there any restrictions on the variable?

Answer 29

\[\frac{ y^2(2+y) }{ y(y+1) }\]
One more simplification, that y^2 and y can be simplified.

Answer 30

\[y^5\div y^3=y^2\]
Subtraction of exponents

Answer 31

So that's our answer? y^2?

Answer 32

No, that was just an example of the formula, lol

Use that to simplify the y^2 on the numerator and y on the botton.

Answer 33

*bottom

Answer 34

\[y^2(2 + y) = y(y + 2) + 1 \] right?

Answer 35

No wait that would make it 2y

Answer 36

I think your thinking too hard.\[\frac{ y^2(2+y) }{ y(y+1) }=\frac{ y(2+y) }{ (y+1) }\]

Answer 37

You can't simplify it any further after that

Answer 38

So this is our restriction of the variable?

Answer 39

\[y^2\div y^1=y\]

Answer 40

Sorry I'm good in English not math

Answer 41

\[\frac{ y(2+y) }{ (y+1) }\]
That answers into the most simplified product of your original question

Answer 42

As for restrictions, that's asking what numbers can't be used

Answer 43

As for as I'm concerned the only restriction for y would be -1, because the denominator is "illegal" if it's 0

Answer 44

Okay I see

Answer 45

So I believe that answers all your questions?

Answer 46

I think so! Thank you so much!

Answer 47

No problem. Feel free to fan and tag me into more questions. Thanks for cooperating through my "lesson"